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max power of 2 that divides \lceil(1+\sqrt{3})^{2n}\rceil for pos. integer n

Source: Gulf Mathematical Olympiad GMO 2017 p4

August 23, 2019

ceiling functionpower of 2dividesmaximumnumber theory

Problem Statement

1 - Prove that

55 < (1+\sqrt{3})^4 < 56

.
2 - Find the largest power of

2

that divides

\lceil(1+\sqrt{3})^{2n}\rceil

for the positive integer

n